This is a study of the efficacy and safety of preladenant in adult participants with moderate to severe Parkinson's Disease (PD). While on this study, participants will continue to take their usual, prescribed, stable regimen of levodopa (L-dopa) or L-dopa plus adjunct PD medications and will be randomized to receive 2 mg preladenant, 5 mg preladenant, or placebo, twice daily, for 12 weeks. After that, participants may choose to receive additional treatment with preladenant. The primary hypothesis is that at least the 5 mg twice daily dose of preladenant is superior to placebo as measured by the change from Baseline to Week 12 in the mean "off" time.